One, two! One, two! And through and through
The vorpal blade went snicker-snack!
He left it dead, and with its head
He went galumphing back.
Closeszcash/pasta_curves#42.
It was only present to enable an FFT implementation in `halo2_proofs`
that is generic over fields and groups, but we can replace it with an
equivalent trait in `halo2_proofs` that can have a blanket impl.
Now that we have a default implementation of `SqrtRatio::sqrt_ratio`, we
can use it and `FieldExt` in no-std environments.
We introduce an `alloc` feature flag to form a common feature dependency
between `std` and `sqrt-table`. It is currently unused directly, but
will be used after `CurveAffine` is refactored to remove the `std`
dependency.
Closeszcash/pasta_curves#25.
It is only used internally by the table-based square root impl, and we
should probably refactor this further, but for now it can live in the
sqrt extension trait.
- `ff::PrimeField::{from_repr, to_repr}` are direct replacements for
`FieldExt::{from_bytes, to_bytes}`.
- `FieldExt::{read, write}` were added for reading and writing `halo2`
proofs, but `halo2::transcript` now handles this internally.
We can use the `ff::PrimeField::root_of_unity` method everywhere we
currently use this associated constant. If there is a more general
need for accessing this as an associated constant, we should consider
that for `ff::PrimeField`.
We re-introduce the Tonelli-Shank square root algoritm that was removed
in zcash/halo2#120, to use in no-std mode (the table-based impl requires
allocations, and also uses 29kiB of memory which is a problem for
constrained environments that typically need no-std).
The previous `CurveAffine::get_xy` method returned the coordinates as
`CtOption<(C::Base, C::Base)>`. However, `ConditionallySelectable` is
not implemented for any tuple or array types, making it impossible to
use any of the useful `CtOption` methods like `and_then`. We replace it
with `CurveAffine::coordinates -> CtOption<Coordinates<Self>>` and
`impl ConditionallySelectable for Coordinates` to enable operating over
coordinates in constant time.
The `Curve` trait is now `CurveExt: group::prime::PrimeCurve`, and
`CurveAffine` is now `CurveAffine: group::prime::PrimeCurveAffine`.
There is no `CurveAffine` trait in `group`, and it's a widely-used
trait in this crate, so we don't rename it to `CurveAffineExt`.
This removes an unnecessary layer of indirection from the type system,
and ensures that these APIs depend on the halo2-specific trait with the
extensions we require.
